Virtual reality or virtually real : blended teaching and learning in a Master's level research methods class

This paper examines the enabling effect of using blended learning and synchronous internet mediated communication technologies to improve learning and develop a Sense of Community (SOC) in a group of post-graduate students consisting of a mix of on-campus and off-campus students. Both quantitative and qualitative data collected over a number of years supports the assertion that the blended learning environment enhanced both teaching and learning. The development of a SOC was pivotal to the success of the blended approach when working with geographically isolated groups within a single learning environment.

Prediction of adjacent vertebral fracture risk associated with vertebroplasty : a computer-based simulation study

Vertebrplasty involved injecting cement into a fractured vertebra to provide stabilisation. There is clinical evidence to suggest however that vertebroplasty may be assocated with a higher risk of adjacent vertebral fracture; which may be due to the change in material properties of the post-procedure vertebra modifying the transmission of mechanical stresses to adjacent vertebrae.

Comparison of methods for processing drinking water samples for the isolation of Myocbacterium avium and intracellulare

Several protocols for isolation of mycobacteria from water exist, but there is no established standard method. This study compared methods of processing potable water samples for the isolation of Mycobacterium avium and Mycobacterium intracellulare using spiked sterilized water and tap water decontaminated using 0.005% cetylpyridinium chloride (CPC). Samples were concentrated by centrifugation or filtration and inoculated onto Middlebrook 7H10 and 7H11 plates and Lowenstein-Jensen slants and into mycobacterial growth indicator tubes with or without polymyxin, azlocillin, nalidixic acid, trimethoprim, and amphotericin B. The solid media were incubated at 32°C, at 35°C, and at 35°C with CO2 and read weekly. The results suggest that filtration of water for the isolation of mycobacteria is a more sensitive method for concentration than centrifugation. The addition of sodium thiosulfate may not be necessary and may reduce the yield. Middlebrook M7H10 and 7H11 were equally sensitive culture media. CPC decontamination, while effective for reducing growth of contaminants, also significantly reduces mycobacterial numbers. There was no difference at 3 weeks between the different incubation temperatures.

Using information criteria to select the correct variance–covariance structure for longitudinal data in ecology

1. Ecological data sets often use clustered measurements or use repeated sampling in a longitudinal design. Choosing the correct covariance structure is an important step in the analysis of such data, as the covariance describes the degree of similarity among the repeated observations. 2. Three methods for choosing the covariance are: the Akaike information criterion (AIC), the quasi-information criterion (QIC), and the deviance information criterion (DIC). We compared the methods using a simulation study and using a data set that explored effects of forest fragmentation on avian species richness over 15 years. 3. The overall success was 80.6% for the AIC, 29.4% for the QIC and 81.6% for the DIC. For the forest fragmentation study the AIC and DIC selected the unstructured covariance, whereas the QIC selected the simpler autoregressive covariance. Graphical diagnostics suggested that the unstructured covariance was probably correct. 4. We recommend using DIC for selecting the correct covariance structure.

Inducing shades of meaning by matrix methods : a first step towards thematic analysis of opinion

This article explores two matrix methods to induce the ``shades of meaning" (SoM) of a word. A matrix representation of a word is computed from a corpus of traces based on the given word. Non-negative Matrix Factorisation (NMF) and Singular Value Decomposition (SVD) compute a set of vectors corresponding to a potential shade of meaning. The two methods were evaluated based on loss of conditional entropy with respect to two sets of manually tagged data. One set reflects concepts generally appearing in text, and the second set comprises words used for investigations into word sense disambiguation. Results show that for NMF consistently outperforms SVD for inducing both SoM of general concepts as well as word senses. The problem of inducing the shades of meaning of a word is more subtle than that of word sense induction and hence relevant to thematic analysis of opinion where nuances of opinion can arise.

How current pedagogy methods in games teaching in the UK, Australia and the US have been shaped by historical, socio cultural, environmental and political constraints

Crucial to enhancing the status and quality of games teaching in schools is a developed understanding of the teaching strategies adopted by practitioners. In this paper, we will demonstrate that contemporary games‟ teaching is a product of individual, task and environmental constraints (Newell, 1986). More specifically, we will show that current pedagogy in the U.K., Australia and the United States is strongly influenced by historical, socio-cultural environmental and political constraints. In summary, we will aim to answer the question „why do teachers teach games the way they do.‟ In answering this question, we conclude that teacher educators, who are trying to influence pedagogical practice, must understand these potential constraints and provide appropriate pre-service experiences to give future physical education teachers the knowledge, confidence and ability to adopt a range of teaching styles when they become fully fledged teachers. Essential to this process is the need to enable future practitioners to base their pedagogical practice on a sound understanding of contemporary learning theories of skill acquisition.

Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion

Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.

Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term

In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moreover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.

Numerical simulation for the 3D seepage flow with fractional derivatives in porous media

In this paper, the numerical simulation of the 3D seepage flow with fractional derivatives in porous media is considered under two special cases: non-continued seepage flow in uniform media (NCSFUM) and continued seepage flow in non-uniform media (CSF-NUM). A fractional alternating direction implicit scheme (FADIS) for the NCSF-UM and a modified Douglas scheme (MDS) for the CSF-NUM are proposed. The stability, consistency and convergence of both FADIS and MDS in a bounded domain are discussed. A method for improving the speed of convergence by Richardson extrapolation for the MDS is also presented. Finally, numerical results are presented to support our theoretical analysis.

Modified alternating direction methods for solving a two-dimensional non-continuous seepage flow with fractional derivatives

In this paper, a two-dimensional non-continuous seepage flow with fractional derivatives (2D-NCSF-FD) in uniform media is considered, which has modified the well known Darcy law. Using the relationship between Riemann-Liouville and Grunwald-Letnikov fractional derivatives, two modified alternating direction methods: a modified alternating direction implicit Euler method and a modified Peaceman-Rachford method, are proposed for solving the 2D-NCSF-FD in uniform media. The stability and consistency, thus convergence of the two methods in a bounded domain are discussed. Finally, numerical results are given.

Evolutionary optimisation methods with uncertainty for modern multidisciplinary design in aeronautical engineering

One of the new challenges in aeronautics is combining and accounting for multiple disciplines while considering uncertainties or variability in the design parameters or operating conditions. This paper describes a methodology for robust multidisciplinary design optimisation when there is uncertainty in the operating conditions. The methodology, which is based on canonical evolution algorithms, is enhanced by its coupling with an uncertainty analysis technique. The paper illustrates the use of this methodology on two practical test cases related to Unmanned Aerial Systems (UAS). These are the ideal candidates due to the multi-physics involved and the variability of missions to be performed. Results obtained from the optimisation show that the method is effective to find useful Pareto non-dominated solutions and demonstrate the use of robust design techniques.

Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

In this paper, we consider the numerical solution of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection–dispersion equation (RFADE). The RFDE is obtained from the standard diffusion equation by replacing the second-order space derivative with the Riesz fractional derivative of order αset membership, variant(1,2]. The RFADE is obtained from the standard advection–dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order βset membership, variant(0,1) and of order αset membership, variant(1,2], respectively. Firstly, analytic solutions of both the RFDE and RFADE are derived. Secondly, three numerical methods are provided to deal with the Riesz space fractional derivatives, namely, the L1/L2-approximation method, the standard/shifted Grünwald method, and the matrix transform method (MTM). Thirdly, the RFDE and RFADE are transformed into a system of ordinary differential equations, which is then solved by the method of lines. Finally, numerical results are given, which demonstrate the effectiveness and convergence of the three numerical methods.

Effects of collimator backscatter in an Elekta linac by Monte Carlo simulation

The effects of radiation backscattered from the secondary collimators into the monitor chamber in an Elekta linac (producing 6 and 10 MV photon beams) are investigated using BEAMnrc Monte Carlo simulations. The degree and effects of this backscattered radiation are assessed by evaluating the changes to the calculated dose in the monitor chamber, and by determining a correction factor for those changes. Additionally, the fluency and energy characteristics of particles entering the monitor chamber from the downstream direction are evaluated by examining BEAMnrc phase-space data. It is shown that the proportion of particles backscattered into the monitor chamber is small (<0.35 %), for all field sizes studied. However, when the backscatter plate is removed from the model linac, these backscattered particles generate a noticeable increase in dose to the monitor chamber (up to approximate to 2.4 % for the 6 MV beam and up to 4.4 % for the 10 MV beam). With its backscatter plate in place, the Elekta linac (operating at 6 and 10 MV) is subject to negligible variation of monitor chamber dose with field size. At these energies, output variations in photon beams produced by the clinical Elekta linear accelerator can be attributed to head scatter alone. Corrections for field-size-dependence of monitor chamber dose are not necessary when running Monte Carlo simulations of the Elekta linac operating at 6 and 10 MV.

Robot path planning in dynamic environments using a simulated annealing based approach

Mobile robots are widely used in many industrial fields. Research on path planning for mobile robots is one of the most important aspects in mobile robots research. Path planning for a mobile robot is to find a collision-free route, through the robot’s environment with obstacles, from a specified start location to a desired goal destination while satisfying certain optimization criteria. Most of the existing path planning methods, such as the visibility graph, the cell decomposition, and the potential field are designed with the focus on static environments, in which there are only stationary obstacles. However, in practical systems such as Marine Science Research, Robots in Mining Industry, and RoboCup games, robots usually face dynamic environments, in which both moving and stationary obstacles exist. Because of the complexity of the dynamic environments, research on path planning in the environments with dynamic obstacles is limited. Limited numbers of papers have been published in this area in comparison with hundreds of reports on path planning in stationary environments in the open literature. Recently, a genetic algorithm based approach has been introduced to plan the optimal path for a mobile robot in a dynamic environment with moving obstacles. However, with the increase of the number of the obstacles in the environment, and the changes of the moving speed and direction of the robot and obstacles, the size of the problem to be solved increases sharply. Consequently, the performance of the genetic algorithm based approach deteriorates significantly. This motivates the research of this work. This research develops and implements a simulated annealing algorithm based approach to find the optimal path for a mobile robot in a dynamic environment with moving obstacles. The simulated annealing algorithm is an optimization algorithm similar to the genetic algorithm in principle. However, our investigation and simulations have indicated that the simulated annealing algorithm based approach is simpler and easier to implement. Its performance is also shown to be superior to that of the genetic algorithm based approach in both online and offline processing times as well as in obtaining the optimal solution for path planning of the robot in the dynamic environment. The first step of many path planning methods is to search an initial feasible path for the robot. A commonly used method for searching the initial path is to randomly pick up some vertices of the obstacles in the search space. This is time consuming in both static and dynamic path planning, and has an important impact on the efficiency of the dynamic path planning. This research proposes a heuristic method to search the feasible initial path efficiently. Then, the heuristic method is incorporated into the proposed simulated annealing algorithm based approach for dynamic robot path planning. Simulation experiments have shown that with the incorporation of the heuristic method, the developed simulated annealing algorithm based approach requires much shorter processing time to get the optimal solutions in the dynamic path planning problem. Furthermore, the quality of the solution, as characterized by the length of the planned path, is also improved with the incorporated heuristic method in the simulated annealing based approach for both online and offline path planning.

Linkage and heritability analysis of migraine symptom groupings: A comparison of three different clustering methods on twin data

Migraine is a painful disorder for which the etiology remains obscure. Diagnosis is largely based on International Headache Society criteria. However, no feature occurs in all patients who meet these criteria, and no single symptom is required for diagnosis. Consequently, this definition may not accurately reflect the phenotypic heterogeneity or genetic basis of the disorder. Such phenotypic uncertainty is typical for complex genetic disorders and has encouraged interest in multivariate statistical methods for classifying disease phenotypes. We applied three popular statistical phenotyping methods—latent class analysis, grade of membership and grade of membership “fuzzy” clustering (Fanny)—to migraine symptom data, and compared heritability and genome-wide linkage results obtained using each approach. Our results demonstrate that different methodologies produce different clustering structures and non-negligible differences in subsequent analyses. We therefore urge caution in the use of any single approach and suggest that multiple phenotyping methods be used.